We consider cyclic ecological systems consisting of more than three species, extending the well-studied three-species rock–paper–scissors (RPS) system. For such systems alliance and partial alliance states consisting of non-competing species can form, a phenomenon not present in classical RPS systems. We develop, analyze and simulate a May–Leonard type model accounting for cyclic dynamics and spatial diffusion. We analyze in detail four-species and five-species systems, determine dynamics for both spatially homogeneous initial conditions (i.e., ode models) and the propagation and interaction of patches of different species driven by diffusion and the cyclic dynamics (pde models). We show markedly different behavior between the four-and five-species models, with alliance states as stable steady states for the former whereas both coexistence of all species and heteroclinic cycles are possible stable outcomes for the latter. Finally, we discuss the extension of this even/odd split to systems with more than five species.

我们考虑了由三种以上物种组成的循环生态系统，扩展了经过深入研究的三种石头剪刀布（RPS）系统。对于这样的系统，可以形成由非竞争性物种组成的联盟和部分联盟状态，这是经典RPS系统中不存在的现象。我们开发，分析和模拟考虑循环动力学和空间扩散的May-Leonard类型模型。我们详细分析了四种和五种系统，确定了空间均质初始条件（即ode模型）的动力学，以及由扩散和循环动力学驱动的不同物种斑块的传播和相互作用（pde模型）。我们展示了四种和五种模型之间明显不同的行为，联盟状态对于前者来说是稳定的稳态，而所有物种的共存和异质循环对于后者来说可能是稳定的结果。最后，我们讨论将这种偶数/奇数拆分扩展到具有五个以上物种的系统。